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%I #7 Dec 28 2024 22:35:26
%S 37,53,67,83,97,157,293,307,353,367,503,547,683,743,757,907,953,967,
%T 983,997,1193,1553,1567,1733,1747,2153,2617,2843,2857,3083,3203,3217,
%U 3307,4057,4133,4283,4297,5107,5153,5167,5303,6143,6397,6607,7253,7417
%N Primes the sum of five consecutive composite numbers.
%H Charles R Greathouse IV, <a href="/A060330/b060330.txt">Table of n, a(n) for n = 1..10000</a>
%t composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); a = {}; Do[ p = composite[ n ] + composite[ n + 1 ] + composite[ n + 2 ] + composite[ n + 3 ] + composite[ n + 4 ]; If[ PrimeQ[ p ], a = Append[ a, p ] ], {n, 1, 1500} ]; a
%o (PARI) list(lim)=my(v=List(),u=[4,6,8,9,0],i=5); forcomposite(n=10,lim\1, u[i]=n; if(i++>5,i=1); my(p=vecsum(u)); if(p>lim, break); if(i++>5,i=1); if(isprime(p), listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Dec 27 2024
%K nonn,changed
%O 1,1
%A _Robert G. Wilson v_, Mar 30 2001